Dont forget about the 14th, they too were a part of the brigade.
Well, the 14th was part of the First or Eastern Iron Brigade. Together with the 2nd US Sharpshooters for example.
They fought mostly side by side with their "sister" brigade, the Western Iron Brigade, which was formed by western regiments of wisconsin or michigan.
Both Iron Brigades are different, but they fought in the same division.